Алгоритми пошуку оптимальної сітки на заданому наборі точок для мінімаксної та середньоквадратичної багатовимірної сплайн-функції на хаотичній сітці
Рік:
2016
Сторінок:
С. 87-94
Тип документу:
Стаття
Головний документ:
Київський Вісник Київського національного університету імені Тараса Шевченка / Київський, університет імені національний; редкол.: голов. ред. Анісімов А.В. ; Хусаінов Д.Я., Arturs Medvids, Miklos Ronto [та ін.]. - Київ, 2016
Анотація:
This is considered the task of data processing: the input is a data stream consisting of discrete measurement values of an unknown multidimensional smooth function in some points of the values of its variables. When processing real measurements data to obtain the most accurate prediction of process behavior, represented by data flow, it is necessary to build a sufficiently robust and accurate computer model that describes the behavior of the process. The article as a model is considered a multidimensional spline function on a chaotic grid of its construction. The article as a model is considered a MSFCG (multidimensional spline function on a chaotic grid) of its construction. We demonstrate the use of such spline functions as the best choice among allthe spline functions at the expense of the simplicity and universality of the model in the form of simple sums of certain functions, which is the only spline function for the entire set definition of variables and requires less computer memory for its construction. But for approximate MSFCG has its own problems. So, to calculate the coefficients we need to find the inverse to of a symmetric dense matrix. On the other hand, by reducing the grid becomes less local optimums MSFCG, it becomes more smoot&h, and can therefore increase the predicted stability of its behavior inside the area bounded by measurement points. Therefore, you should build a spline function with a minimum number of points of the grid. And to this spline function has been fairl&y accurate throughout the dataset. Constructed four algorithms for finding an optimal grid of approximate MSFCG by exclusion and inclusion of points grid. Accuracy approximation of random data - the absolute and the mean. Points for the grid are sele&cted from a discrete finite set of available measurements. Optimum grid understood as the minimum number of points for a given accuracy of approximation spline-function at all points available measurements.
